A bending device for forming a corrugation in a metal sheet, the bending device having a frame, a die having two die elements, each having a concave half-impression, mounted able to slide on the frame; a punch having a head able to engage inside the impression of the die so as to press the metal sheet; and two side clamps mounted sliding and able to move vertically with respect to the lower frame so as to clamp the metal sheet against the bearing surfaces of the die elements. During the displacement of the punch into its bending position, the metal sheet transmits a traction force to the die elements and to the side clamps so as to displace them into their near position.